One theory is that the drink was named after British Royal Navy Surgeon General Sir Thomas D. Gimlette, KCB (served 1879 to 1913), who allegedly introduced this drink as a means of inducing his messmates to take lime juice as an anti-scurvy medication. Limes and other citrus fruit have been used by the Royal Navy for the treatment of scurvy since the mid-18th century.
Fill a shaker with ice cubes. Add all ingredients. Stir and strain into a chilled cocktail glass. Garnish with lime.